Question: Simplify the following expression: $ n = \dfrac{-4}{3} - \dfrac{2}{6k + 8} $
Explanation: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{6k + 8}{6k + 8}$ $ \dfrac{-4}{3} \times \dfrac{6k + 8}{6k + 8} = \dfrac{-24k - 32}{18k + 24} $ Multiply the second expression by $\dfrac{3}{3}$ $ \dfrac{2}{6k + 8} \times \dfrac{3}{3} = \dfrac{6}{18k + 24} $ Therefore $ n = \dfrac{-24k - 32}{18k + 24} - \dfrac{6}{18k + 24} $ Now the expressions have the same denominator we can simply subtract the numerators: $n = \dfrac{-24k - 32 - 6 }{18k + 24} $ Distribute the negative sign: $n = \dfrac{-24k - 32 - 6}{18k + 24}$ $n = \dfrac{-24k - 38}{18k + 24}$ Simplify the expression by dividing the numerator and denominator by 2: $n = \dfrac{-12k - 19}{9k + 12}$